Related papers: Tagged vector space, Part I: Dirac notation as ori…
We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained.
As shown in earlier work, skew-adjoint linear differential operators, mapping efforts into flows, give rise to Dirac structures on a bounded spatial domain by a proper definition of boundary variables. In the present paper this is extended…
We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or…
This note discusses the Wigner function representation from the standpoint of establishing a holography-like correspondence between the descriptions of a generic quantum system in the phase space ('bulk') picture versus its spacetime…
The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint…
The paper describes a unique phenomenon -- the possibility of establishing, in certain space regions, the one-to-one correspondence between equations related to absolutely different physical phenomena: (1) phenomena associated with the Weyl…
Phase spaces as given by the Wigner distribution function provide a natural description of infinite-dimensional quantum systems. They are an important tool in quantum optics and have been widely applied in the context of time-frequency…
Classical model of light in helicity formalism is presented. Then quantum point of view at photons -- construction and interpretation of photon wave function is proposed. Quantum mechanics of photon is investigated. The Bia\l ynicki --…
We first generalise the standard Wigner function to Dirac fermions in curved spacetimes. Secondly, we turn to the Moyal quantisation of systems with constraints. Gravity is used as an example.
We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of…
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
We introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we a series of representations…
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of…
The purpose of this paper is to explore, in a space of four-dimensions, the possible forms that second-order, bi-scalar-vector-tensor field equations derivable from a variational principle can assume. In order to restrict this enormous…
The conditions under which a given manifold $M$ may be given a tangent bundle or a cotangent bundle structure are analyzed. This is an important property arising in different contexts. For instance, in the study of integrability of a given…
The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary…
The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional…
The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and…
The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein--Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the…
The paper scrutinizes both the similarities and the differences between the classical optics and quantum mechanical theories in phase space, especially between the Wigner distribution functions defined in the respective phase spaces.…